ON THE MINKOWSKI DIMENSION OF CERTAIN KAKEYA SETS

Abstract

The Kakeya conjecture states that all compact subsets of \(\mathbb{R}^n\) containing a unit line segment in every direction have full Hausdorff dimension. The analogue of the Kakeya conjecture with \(\mathbb{R}^n\) replaced by \(\mathbb{R}_p^n\) was recently proved in [1]. An earlier draft of that article proved a special case concerning Minkowski dimension by using a more specialized combinatorial argument. The referees for [1] suggested that this is of independent interest, and that it should be published as a separate article. Thus, this article documents that argument.